Plot of Albuquerque Data

Here is my plot of Albuquerque maximum temperatures overlayed with a best fit line:

Lets look at some of the results for this regression:

## 
## Call:
## lm(formula = TMAX ~ DATES, data = climate_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -35.689  -8.106   0.825   8.728  20.295 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 2.128e+01  5.608e-02 379.530   <2e-16 ***
## DATES       1.356e-05  5.931e-06   2.287   0.0222 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.85 on 32105 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.0001629,  Adjusted R-squared:  0.0001317 
## F-statistic:  5.23 on 1 and 32105 DF,  p-value: 0.02221

Note that the p-value for the y-intercept is 2x10^-6 and the p-value for the slope of the line is .02. Both of these values are less than .05. In other words, we can say with 95% confidence that our temperature is increasing at a rate of 1.356x10^-5 degrees C per year and has an intercept of 21.28 degrees C.

Let’s go ahead and clean up our original graph by looking at monthly averages one month at a time.

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9898 -1.4768 -0.0783  1.8627  4.2359 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -28.60050   16.91257  -1.691   0.0944 .
## YEAR          0.01882    0.00856   2.198   0.0306 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.04 on 86 degrees of freedom
## Multiple R-squared:  0.05319,    Adjusted R-squared:  0.04218 
## F-statistic: 4.831 on 1 and 86 DF,  p-value: 0.03063

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.3104 -1.4311  0.0408  1.6153  4.7256 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -25.027639  18.641886  -1.343   0.1830  
## YEAR          0.018737   0.009438   1.985   0.0503 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.211 on 85 degrees of freedom
## Multiple R-squared:  0.04431,    Adjusted R-squared:  0.03307 
## F-statistic: 3.941 on 1 and 85 DF,  p-value: 0.05034

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0155 -1.3019 -0.1369  1.1707  5.4288 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -41.103197  15.697489  -2.618 0.010437 *  
## YEAR          0.029099   0.007949   3.661 0.000434 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.894 on 86 degrees of freedom
## Multiple R-squared:  0.1348, Adjusted R-squared:  0.1247 
## F-statistic:  13.4 on 1 and 86 DF,  p-value: 0.0004336

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1130 -0.8838 -0.2057  1.1431  3.9821 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  6.495014  14.479181   0.449    0.655
## YEAR         0.007533   0.007332   1.027    0.307
## 
## Residual standard error: 1.747 on 86 degrees of freedom
## Multiple R-squared:  0.01212,    Adjusted R-squared:  0.0006364 
## F-statistic: 1.055 on 1 and 86 DF,  p-value: 0.3071

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.4346 -1.1179 -0.1707  0.9689  3.9850 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.116514  13.179305   0.919    0.360
## YEAR         0.007294   0.006674   1.093    0.277
## 
## Residual standard error: 1.59 on 86 degrees of freedom
## Multiple R-squared:  0.0137, Adjusted R-squared:  0.002231 
## F-statistic: 1.195 on 1 and 86 DF,  p-value: 0.2775

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1216 -0.8659 -0.0342  0.7996  3.4784 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -2.720334  11.253071  -0.242  0.80956   
## YEAR         0.017713   0.005699   3.108  0.00255 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.358 on 86 degrees of freedom
## Multiple R-squared:  0.101,  Adjusted R-squared:  0.09054 
## F-statistic: 9.661 on 1 and 86 DF,  p-value: 0.002551

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3136 -0.8437 -0.1187  0.6718  3.9363 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 37.812784  10.078899   3.752 0.000318 ***
## YEAR        -0.002250   0.005104  -0.441 0.660412    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.216 on 86 degrees of freedom
## Multiple R-squared:  0.002255,   Adjusted R-squared:  -0.009347 
## F-statistic: 0.1944 on 1 and 86 DF,  p-value: 0.6604

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1766 -0.7669 -0.0452  0.8890  2.7807 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 45.528318  10.006676   4.550 1.75e-05 ***
## YEAR        -0.006950   0.005068  -1.372    0.174    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.208 on 86 degrees of freedom
## Multiple R-squared:  0.0214, Adjusted R-squared:  0.01003 
## F-statistic: 1.881 on 1 and 86 DF,  p-value: 0.1738

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.7412 -1.1391  0.0648  1.0468  3.5288 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 32.616378  11.784895   2.768  0.00691 **
## YEAR        -0.002266   0.005968  -0.380  0.70514   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.422 on 86 degrees of freedom
## Multiple R-squared:  0.001673,   Adjusted R-squared:  -0.009935 
## F-statistic: 0.1441 on 1 and 86 DF,  p-value: 0.7051

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.3097 -1.3341  0.0656  1.2140  5.0281 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)   
## (Intercept) 39.293470  14.869752   2.643  0.00978 **
## YEAR        -0.008848   0.007530  -1.175  0.24323   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.794 on 86 degrees of freedom
## Multiple R-squared:  0.0158, Adjusted R-squared:  0.004356 
## F-statistic: 1.381 on 1 and 86 DF,  p-value: 0.2432

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.8360 -1.2418  0.1803  1.1735  4.8920 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  3.320367  15.829233    0.21    0.834
## YEAR         0.005449   0.008016    0.68    0.498
## 
## Residual standard error: 1.91 on 86 degrees of freedom
## Multiple R-squared:  0.005345,   Adjusted R-squared:  -0.006221 
## F-statistic: 0.4621 on 1 and 86 DF,  p-value: 0.4985

## 
## Call:
## lm(formula = TMAX ~ YEAR, data = MonthlyTMAXMean[MonthlyTMAXMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8498 -1.1722 -0.1227  1.3387  4.2202 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 18.554731  16.036793   1.157    0.250
## YEAR        -0.004923   0.008121  -0.606    0.546
## 
## Residual standard error: 1.935 on 86 degrees of freedom
## Multiple R-squared:  0.004255,   Adjusted R-squared:  -0.007323 
## F-statistic: 0.3675 on 1 and 86 DF,  p-value: 0.546

Ok cool. Let’s do the same thing except for TMIN data now instead.

Lets look at some of the results for this regression:

## 
## Call:
## lm(formula = TMIN ~ DATES, data = climate_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -33.630  -7.494  -0.223   8.325  18.334 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 6.404e+00  5.044e-02  126.97   <2e-16 ***
## DATES       7.037e-05  5.334e-06   13.19   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.859 on 32105 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.005392,   Adjusted R-squared:  0.005361 
## F-statistic:   174 on 1 and 32105 DF,  p-value: < 2.2e-16

[SOME ANALYSIS] Let’s go ahead and clean up our original graph by looking at monthly averages one month at a time.

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -5.121 -1.257 -0.108  1.349  4.224 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -71.850088  15.977413  -4.497 2.14e-05 ***
## YEAR          0.034087   0.008087   4.215 6.14e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.927 on 86 degrees of freedom
## Multiple R-squared:  0.1712, Adjusted R-squared:  0.1616 
## F-statistic: 17.77 on 1 and 86 DF,  p-value: 6.145e-05

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.1934 -1.0198 -0.0768  0.9996  5.6681 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -66.064772  16.069852  -4.111 9.05e-05 ***
## YEAR          0.032296   0.008136   3.970  0.00015 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.906 on 85 degrees of freedom
## Multiple R-squared:  0.1564, Adjusted R-squared:  0.1465 
## F-statistic: 15.76 on 1 and 85 DF,  p-value: 0.00015

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3844 -0.8691  0.1963  0.9490  3.0536 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -75.898882  11.538049  -6.578 3.55e-09 ***
## YEAR          0.038882   0.005843   6.654 2.52e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.392 on 86 degrees of freedom
## Multiple R-squared:  0.3399, Adjusted R-squared:  0.3322 
## F-statistic: 44.28 on 1 and 86 DF,  p-value: 2.525e-09

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1211 -0.7839  0.0959  0.9470  4.6590 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -43.754036  13.297688  -3.290 0.001452 ** 
## YEAR          0.024765   0.006734   3.678 0.000409 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.605 on 86 degrees of freedom
## Multiple R-squared:  0.1359, Adjusted R-squared:  0.1258 
## F-statistic: 13.52 on 1 and 86 DF,  p-value: 0.0004093

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.6786 -0.9287  0.1068  1.1252  2.4969 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -33.786160  12.238223  -2.761 0.007049 ** 
## YEAR          0.022297   0.006198   3.598 0.000535 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.477 on 86 degrees of freedom
## Multiple R-squared:  0.1308, Adjusted R-squared:  0.1207 
## F-statistic: 12.94 on 1 and 86 DF,  p-value: 0.0005354

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1994 -1.0735 -0.1924  0.8488  3.2773 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -51.274069  11.224752  -4.568 1.63e-05 ***
## YEAR          0.033846   0.005684   5.954 5.54e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.355 on 86 degrees of freedom
## Multiple R-squared:  0.2919, Adjusted R-squared:  0.2837 
## F-statistic: 35.45 on 1 and 86 DF,  p-value: 5.541e-08

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.25029 -0.68049  0.01608  0.53894  2.62266 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -24.80398    7.60250  -3.263  0.00158 ** 
## YEAR          0.02190    0.00385   5.687 1.74e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9174 on 86 degrees of freedom
## Multiple R-squared:  0.2733, Adjusted R-squared:  0.2648 
## F-statistic: 32.34 on 1 and 86 DF,  p-value: 1.743e-07

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.09133 -0.63185  0.03808  0.53974  2.11021 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -17.158922   7.409235  -2.316   0.0229 *  
## YEAR          0.017570   0.003752   4.683 1.05e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8941 on 86 degrees of freedom
## Multiple R-squared:  0.2032, Adjusted R-squared:  0.1939 
## F-statistic: 21.93 on 1 and 86 DF,  p-value: 1.049e-05

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.3999 -0.8945  0.1578  0.9943  2.4423 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -26.352264  10.398567  -2.534 0.013081 *  
## YEAR          0.020289   0.005266   3.853 0.000224 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.255 on 86 degrees of freedom
## Multiple R-squared:  0.1472, Adjusted R-squared:  0.1373 
## F-statistic: 14.84 on 1 and 86 DF,  p-value: 0.0002244

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4268 -0.8014  0.0885  1.0423  4.0343 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -35.222087  11.800345  -2.985 0.003694 ** 
## YEAR          0.021392   0.005976   3.580 0.000569 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.424 on 86 degrees of freedom
## Multiple R-squared:  0.1297, Adjusted R-squared:  0.1196 
## F-statistic: 12.81 on 1 and 86 DF,  p-value: 0.0005686

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.1755 -0.6861  0.0688  0.7318  2.9373 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -73.634316  12.187575  -6.042 3.79e-08 ***
## YEAR          0.037306   0.006172   6.044 3.74e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.471 on 86 degrees of freedom
## Multiple R-squared:  0.2982, Adjusted R-squared:   0.29 
## F-statistic: 36.54 on 1 and 86 DF,  p-value: 3.744e-08

## 
## Call:
## lm(formula = TMIN ~ YEAR, data = MonthlyTMINMean[MonthlyTMINMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8536 -1.0239  0.1069  0.8080  3.3587 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept) -40.380523  12.413131  -3.253  0.00163 **
## YEAR          0.018462   0.006286   2.937  0.00425 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.498 on 86 degrees of freedom
## Multiple R-squared:  0.09116,    Adjusted R-squared:  0.08059 
## F-statistic: 8.626 on 1 and 86 DF,  p-value: 0.004252

Ok lets take a break from all this temprature stuff and look at precipitation instead.

## 
## Call:
## lm(formula = PRCP ~ DATES, data = climate_data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -0.628 -0.614 -0.600 -0.586 48.205 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 6.021e-01  1.420e-02  42.410   <2e-16 ***
## DATES       1.451e-06  1.502e-06   0.966    0.334    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.494 on 32105 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  2.907e-05,  Adjusted R-squared:  -2.077e-06 
## F-statistic: 0.9333 on 1 and 32105 DF,  p-value: 0.334

[SOME ANALYSIS] Let’s go ahead and clean up our original graph by looking at monthly averages one month at a time.

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.32870 -0.22164 -0.07728  0.15257  0.80618 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.2588363  2.3338247  -0.111    0.912
## YEAR         0.0002917  0.0011813   0.247    0.806
## 
## Residual standard error: 0.2815 on 86 degrees of freedom
## Multiple R-squared:  0.0007087,  Adjusted R-squared:  -0.01091 
## F-statistic: 0.06099 on 1 and 86 DF,  p-value: 0.8055

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41037 -0.21722 -0.07784  0.13403  1.26236 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.444710   2.795373  -0.875    0.384
## YEAR         0.001421   0.001415   1.004    0.318
## 
## Residual standard error: 0.3315 on 85 degrees of freedom
## Multiple R-squared:  0.01172,    Adjusted R-squared:  9.686e-05 
## F-statistic: 1.008 on 1 and 85 DF,  p-value: 0.3182

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.40001 -0.27495 -0.05395  0.12151  1.52118 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.1674930  3.1514270  -0.053    0.958
## YEAR         0.0002815  0.0015959   0.176    0.860
## 
## Residual standard error: 0.3803 on 86 degrees of freedom
## Multiple R-squared:  0.0003616,  Adjusted R-squared:  -0.01126 
## F-statistic: 0.03111 on 1 and 86 DF,  p-value: 0.8604

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.4430 -0.3746 -0.1303  0.1628  2.1182 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  1.140537   4.114377   0.277    0.782
## YEAR        -0.000357   0.002084  -0.171    0.864
## 
## Residual standard error: 0.4965 on 86 degrees of freedom
## Multiple R-squared:  0.0003412,  Adjusted R-squared:  -0.01128 
## F-statistic: 0.02935 on 1 and 86 DF,  p-value: 0.8644

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5895 -0.3430 -0.1631  0.1220  1.9195 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  8.174908   4.381272   1.866   0.0655 .
## YEAR        -0.003906   0.002219  -1.760   0.0819 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5287 on 86 degrees of freedom
## Multiple R-squared:  0.03478,    Adjusted R-squared:  0.02356 
## F-statistic: 3.099 on 1 and 86 DF,  p-value: 0.08189

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.6167 -0.3914 -0.1864  0.2100  2.5908 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept)  5.730782   4.721300   1.214    0.228
## YEAR        -0.002637   0.002391  -1.103    0.273
## 
## Residual standard error: 0.5697 on 86 degrees of freedom
## Multiple R-squared:  0.01395,    Adjusted R-squared:  0.002487 
## F-statistic: 1.217 on 1 and 86 DF,  p-value: 0.2731

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.12039 -0.54223 -0.09456  0.46470  1.60949 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)  
## (Intercept) -9.596604   5.663067  -1.695   0.0938 .
## YEAR         0.005447   0.002868   1.899   0.0609 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6834 on 86 degrees of freedom
## Multiple R-squared:  0.04026,    Adjusted R-squared:  0.0291 
## F-statistic: 3.607 on 1 and 86 DF,  p-value: 0.06088

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2007 -0.5919 -0.1190  0.5910  1.8927 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  2.4929329  6.3526572   0.392    0.696
## YEAR        -0.0006586  0.0032171  -0.205    0.838
## 
## Residual standard error: 0.7666 on 86 degrees of freedom
## Multiple R-squared:  0.0004871,  Adjusted R-squared:  -0.01114 
## F-statistic: 0.04191 on 1 and 86 DF,  p-value: 0.8383

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8806 -0.4796 -0.1026  0.2953  2.4001 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.773380   5.067820  -0.547    0.586
## YEAR         0.001855   0.002566   0.723    0.472
## 
## Residual standard error: 0.6116 on 86 degrees of freedom
## Multiple R-squared:  0.006035,   Adjusted R-squared:  -0.005522 
## F-statistic: 0.5222 on 1 and 86 DF,  p-value: 0.4719

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8059 -0.4904 -0.2181  0.3535  1.8356 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.015153   5.398149  -0.929    0.355
## YEAR         0.002893   0.002734   1.058    0.293
## 
## Residual standard error: 0.6514 on 86 degrees of freedom
## Multiple R-squared:  0.01286,    Adjusted R-squared:  0.001378 
## F-statistic:  1.12 on 1 and 86 DF,  p-value: 0.2929

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41004 -0.31896 -0.07345  0.20705  1.23717 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.6268229  3.1019411  -0.202    0.840
## YEAR         0.0005138  0.0015709   0.327    0.744
## 
## Residual standard error: 0.3743 on 86 degrees of freedom
## Multiple R-squared:  0.001242,   Adjusted R-squared:  -0.01037 
## F-statistic: 0.107 on 1 and 86 DF,  p-value: 0.7444

## 
## Call:
## lm(formula = PRCP ~ YEAR, data = MonthlyPRCPMean[MonthlyPRCPMean$MONTH == 
##     i, ])
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.47023 -0.28094 -0.08435  0.22301  1.12223 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.184282   2.996524  -0.729    0.468
## YEAR         0.001316   0.001517   0.867    0.388
## 
## Residual standard error: 0.3616 on 86 degrees of freedom
## Multiple R-squared:  0.00867,    Adjusted R-squared:  -0.002857 
## F-statistic: 0.7522 on 1 and 86 DF,  p-value: 0.3882

Sources to look at: https://onlinelibrary.wiley.com/doi/full/10.1002/eco.1849 http://adsabs.harvard.edu/abs/2016AGUFMGC32C..04S https://onlinelibrary.wiley.com/doi/full/10.1111/gcb.12743 https://www.sciencedirect.com/science/article/pii/S0190052816300323 https://bioone.org/journals/Rangelands/volume-30/issue-3/1551-501X(2008)30[23:CCAEOT]2.0.CO;2/Climate-Change-and-Ecosystems-of-the-Southwestern-United-States/10.2111/1551-501X(2008)30[23:CCAEOT]2.0.CO;2.full https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2008GL035075